In a memo to the staff, the new CEO, Michael Corbat, said he's going to study up over the "the next several weeks" to understand Citigroup's business and then "these assessments will result in some changes."

Citi employees are widely believed to have responded en masse by saying: "Yikes!"

George, in the CNBC interview, said that the making such a sudden change in leadership simply is not done at big, important banks.

"This is not the way boards do things," he said. Usually, a top management change is announced months before it takes effect, giving investors, customers and employees time to absorb and assess the news, he said.

The announcement came one day after the company reported third-quarter earnings that, aside from some one-time items, were seen as very positive. High-speed stock traders jumped in as soon as markets opened today, sending the stock price a bit higher on heavy volume.

Pandit, an Indian-born American, had been the CEO of Citigroup since December, 2007 — a tough time to start. That was the month that the Great Recession officially began.